[[http://cadia.ru.is/wiki/public:t-720-atai:atai-18:main|T-720-ATAI-2018 Main]] \\ [[http://cadia.ru.is/wiki/public:t-720-atai:atai-18:Lecture_Notes|Links to Lecture Notes]] =====T-720-ATAI-2018===== ==== Lecture Notes, W11: Probabilities, Causation & Experience-Based Learning ==== \\ \\ \\ \\ ====Experience-Based Learning==== | What It Is | Learning is the acquisition of knowledge for particular purposes. When this acquisition happens via interaction with an environment it is experience-based. | | Why It Is Important | Any environment which cannot be fully known a-priori requires experimentation of some sort, in the form of interaction with the world. This is what we call //experience//. | | The Real World | The physical world we live in, often referred to as the "real world", is highly complex, and rarely if ever do we have perfect models of how it behaves when we interact with it, whether it is to experiment with how it works or simply achieve some goal like buying bread. | | Limited Time & Resources | An important limitation on any agent's ability to model the real world is its enormous state space, which vastly outdoes any known agent's memory capacity, even for relatively simple environments. Even if the models were sufficiently detailed, pre-computing everything beforehand is prohibited due to memory. On top of that, even if memory would suffice for pre-computing everything and anything necessary to go about our tasks, we would have to retrieve the pre-computed data in time when it's needed - the larger the state space the more demands on retrieval times this puts. | \\ \\ ==== Probability ==== | What It Is | Probability is the measure of the likelihood that an event will occur [[https://en.wikipedia.org/wiki/Probability|REF]]. | | Why It Is Important | Probability enters into our knowledge of anything for which the knowledge is incomplete. As in, everything that humans do every day in every real-world environment. With incomplete knowledge it is in principle impossible to know what may happen. However, if we have very good models for some limited phenomenon, we can expect our prediction of what may happen to be pretty good. This is especially true for knowledge acquired through the scientific method, in which empirical evidence and human reason is systematically brought to bear on the validity of the models. | | How To Do It | Most common method is Bayesian networks, which encode the concept of probability in which probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief [[https://en.wikipedia.org/wiki/Bayesian_probability|REF]]. Which makes it ideal for representing an (intelligent) agent's knowledge of some environment, task or phenomenon [[]]. | | How It Works | P(a|b)={P(b|a)P(a)}/{P(b)} | | Judea Pearl | Most Fervent Advocate of Bayesian Networks in AI [[http://ftp.cs.ucla.edu/pub/stat_ser/R246.pdf|REF]]. | \\ \\ ==== Causation ==== | What It Is | A causal variable can (informally) be defined as a variable whose relationship with another variable is such that when changed it will change the other variable. \\ Example: A light switch is designed specifically to //cause// the light to turn on and off. \\ In //a causal analysis// based on **abduction** one may reason that, given that light switches don't tend to flip randomly, a light that was **off** but is now **on** may indicate that someone or something flipped the light switch. (The inverse - a light that was on but is now off - has a larger set of reasonable causes, in addition to someone turning it off, a power outage or bulb burnout. | | Why It Is Important | Causation is the foundation of empirical science. Without knowledge about causal relations it is impossible to get anything done. | | History | David Hume (1711-1776) is one of the most influential philosophers addressing the topic. From the Encyclopedia of Philosophy: "...advocate[s] ... that there are no innate ideas and that all knowledge comes from experience, Hume is known for applying this standard rigorously to causation and necessity." [[https://www.iep.utm.edu/hume-cau/|REF]] \\ This makes Hume an //empiricist.// | | More Recent History | Causation has been cast by the wayside in statistics for the past 120 years, saying instead that all we can claim about the relationship of any variables is that they correlate. Needless to say this has lead to significant confusion as to what science can and cannot say about causal relationships, such as whether mobile phones cause cancer. Equally badly, the statistical stance has infected some scientific fields to view causation as "unscientific". \\ c.f. [[http://ftp.cs.ucla.edu/pub/stat_ser/r284-reprint.pdf|BAYESIANISM AND CAUSALITY, OR, WHY I AM ONLY A HALF-BAYESIAN]] by J. Pearl | | State Of The Art | Recent work by Judea Pearl demonstrates clearly the fallaciousness of the statistical stance, and fixes some important gaps in our knowledge on this subject which hopefully will rectify the situation in the coming years. [[https://www.youtube.com/watch?v=8nHVUFqI0zk|YouTube lecture by J. Pearl on causation]]. | | Correlation Supports Prediction | While correlation is sufficient for prediction (if A and B correlate highly, then it does not matter if we see an A //OR// a B, we can predict that the other is likely on the scent. | | Causation Supports Action | We may know that A and B correlate, but if we want B to disappear we don't know whether to do that by modifying A or B, because we don't know if B is a result of A or vice versa. \\ //Example: The position of the light switch and the state of the lightbulb correlate. Only by knowing that the light switch controls the bulb can we go directly to the switch if we want the light to turn on. // | | **Causal Models** Are Necessary To Guide Action | While correlation gives us indication of causation, the direction of the "causal arrow" is critically necessary for guiding action. \\ Luckily, knowing which way the arrows point in any large set of correlated variables is usually not too hard to find out, by empirical experimentation. | | Causation & Correlation | What is the relation between causation and correlation? \\ There is no (non-spurious) correlation without causation. \\ There is no causation without correlation. \\ However, causation between two variables does necessitate one of them to be the cause of the other: They can have a shared (possibly hidden) //common cause//. | \\ \\ \\ \\ ------------ 2018(c)K. R. Thórisson //EOF//